A gas turbine engine generally includes a compressor section, a combustion section, a turbine section, and an exhaust section. The compressor section progressively increases the pressure of a working fluid entering the gas turbine engine and supplies this compressed working fluid to the combustion section. The compressed working fluid and a fuel (e.g., natural gas) mix within the combustion section and burn in a combustion chamber to generate high pressure and high temperature combustion gases. The combustion gases flow from the combustion section into the turbine section where they expand to produce work. For example, expansion of the combustion gases in the turbine section may rotate a rotor shaft connected, e.g., to a generator to produce electricity. The combustion gases then exit the gas turbine via the exhaust section.
The turbine section includes a plurality of rotor blades, which extract kinetic energy and/or thermal energy from the combustion gases flowing therethrough. In certain embodiments, some or all of the plurality of rotor blades include a tip shroud coupled to an airfoil portion by a fillet portion. These rotor blades generally operate in extremely high temperature environments. As such, the rotor blades typically include one or more cooling passages defined therein. During operation of the gas turbine engine, a cooling medium such as compressed air flows through the one or more cooling passages to cool the rotor blade. Nevertheless, the conventional cooling passage configurations that provide adequate cooling to the fillet portion and the tip shroud increase the weight of the rotor blade, which may be undesirable.